Transforming Image Into Custom Shape

In recent versions of Illustrator you may also create an Art Brush out of the raster image and apply it to any path.

With the Art Brush options dialog you then get some more options to experiment and adjust the final appearance.

Hi, everything monica said +

You can start with a shape and keep on distorting point

Or you can start with a mesh, where you'll be able to ajust both fidelity and rows/columns :

While choosing the mesh version, don't hesitate to try "mesh tormentor", a free plugin that will help straighten and balance your handles: http://www.meshtormentor.com/

Make sure that circle thing has more than 4 anchor points.

Select the anchor points marked in this picture using the direct selection tool:

Use Object > Make gradient mesh

Create a mesh

Then select the picture and the mesh (mesh on top)

and Object > Envelope > Make with top object